impls/bddc/bddcgraph.c

#include <petsc/private/petscimpl.h>
#include <petsc/private/pcbddcprivateimpl.h>
#include <petsc/private/pcbddcstructsimpl.h>

PetscErrorCode PCBDDCDestroyGraphCandidatesIS(void *ctx) {
  PCBDDCGraphCandidates cand = (PCBDDCGraphCandidates)ctx;

  PetscFunctionBegin;
  for (PetscInt i = 0; i < cand->nfc; i++) PetscCall(ISDestroy(&cand->Faces[i]));
  for (PetscInt i = 0; i < cand->nec; i++) PetscCall(ISDestroy(&cand->Edges[i]));
  PetscCall(PetscFree(cand->Faces));
  PetscCall(PetscFree(cand->Edges));
  PetscCall(ISDestroy(&cand->Vertices));
  PetscCall(PetscFree(cand));
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphGetDirichletDofsB(PCBDDCGraph graph, IS *dirdofs) {
  PetscFunctionBegin;
  if (graph->dirdofsB) {
    PetscCall(PetscObjectReference((PetscObject)graph->dirdofsB));
  } else if (graph->has_dirichlet) {
    PetscInt  i, size;
    PetscInt *dirdofs_idxs;

    size = 0;
    for (i = 0; i < graph->nvtxs; i++) {
      if (graph->count[i] && graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) size++;
    }

    PetscCall(PetscMalloc1(size, &dirdofs_idxs));
    size = 0;
    for (i = 0; i < graph->nvtxs; i++) {
      if (graph->count[i] && graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) dirdofs_idxs[size++] = i;
    }
    PetscCall(ISCreateGeneral(PETSC_COMM_SELF, size, dirdofs_idxs, PETSC_OWN_POINTER, &graph->dirdofsB));
    PetscCall(PetscObjectReference((PetscObject)graph->dirdofsB));
  }
  *dirdofs = graph->dirdofsB;
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphGetDirichletDofs(PCBDDCGraph graph, IS *dirdofs) {
  PetscFunctionBegin;
  if (graph->dirdofs) {
    PetscCall(PetscObjectReference((PetscObject)graph->dirdofs));
  } else if (graph->has_dirichlet) {
    PetscInt  i, size;
    PetscInt *dirdofs_idxs;

    size = 0;
    for (i = 0; i < graph->nvtxs; i++) {
      if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) size++;
    }

    PetscCall(PetscMalloc1(size, &dirdofs_idxs));
    size = 0;
    for (i = 0; i < graph->nvtxs; i++) {
      if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK) dirdofs_idxs[size++] = i;
    }
    PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)graph->l2gmap), size, dirdofs_idxs, PETSC_OWN_POINTER, &graph->dirdofs));
    PetscCall(PetscObjectReference((PetscObject)graph->dirdofs));
  }
  *dirdofs = graph->dirdofs;
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphASCIIView(PCBDDCGraph graph, PetscInt verbosity_level, PetscViewer viewer) {
  PetscInt  i, j, tabs;
  PetscInt *queue_in_global_numbering;

  PetscFunctionBegin;
  PetscCall(PetscViewerASCIIPushSynchronized(viewer));
  PetscCall(PetscViewerASCIIGetTab(viewer, &tabs));
  PetscCall(PetscViewerASCIIPrintf(viewer, "--------------------------------------------------\n"));
  PetscCall(PetscViewerFlush(viewer));
  PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "Local BDDC graph for subdomain %04d\n", PetscGlobalRank));
  PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "Number of vertices %" PetscInt_FMT "\n", graph->nvtxs));
  PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "Number of local subdomains %" PetscInt_FMT "\n", graph->n_local_subs ? graph->n_local_subs : 1));
  PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "Custom minimal size %" PetscInt_FMT "\n", graph->custom_minimal_size));
  if (graph->maxcount != PETSC_MAX_INT) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "Max count %" PetscInt_FMT "\n", graph->maxcount));
  PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "Topological two dim? %s (set %s)\n", PetscBools[graph->twodim], PetscBools[graph->twodimset]));
  if (verbosity_level > 2) {
    for (i = 0; i < graph->nvtxs; i++) {
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "%" PetscInt_FMT ":\n", i));
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   which_dof: %" PetscInt_FMT "\n", graph->which_dof[i]));
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   special_dof: %" PetscInt_FMT "\n", graph->special_dof[i]));
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   neighbours: %" PetscInt_FMT "\n", graph->count[i]));
      PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
      if (graph->count[i]) {
        PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "     set of neighbours:"));
        for (j = 0; j < graph->count[i]; j++) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %" PetscInt_FMT, graph->neighbours_set[i][j]));
        PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\n"));
      }
      PetscCall(PetscViewerASCIISetTab(viewer, tabs));
      PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
      if (graph->mirrors) {
        PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   mirrors: %" PetscInt_FMT "\n", graph->mirrors[i]));
        if (graph->mirrors[i]) {
          PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
          PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "     set of mirrors:"));
          for (j = 0; j < graph->mirrors[i]; j++) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %" PetscInt_FMT, graph->mirrors_set[i][j]));
          PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\n"));
          PetscCall(PetscViewerASCIISetTab(viewer, tabs));
          PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
        }
      }
      if (verbosity_level > 3) {
        if (graph->xadj) {
          PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   local adj list:"));
          PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
          for (j = graph->xadj[i]; j < graph->xadj[i + 1]; j++) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %" PetscInt_FMT, graph->adjncy[j]));
          PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\n"));
          PetscCall(PetscViewerASCIISetTab(viewer, tabs));
          PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
        } else {
          PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   no adj info\n"));
        }
      }
      if (graph->n_local_subs) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   local sub id: %" PetscInt_FMT "\n", graph->local_subs[i]));
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   interface subset id: %" PetscInt_FMT "\n", graph->subset[i]));
      if (graph->subset[i] && graph->subset_ncc) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "   ncc for subset: %" PetscInt_FMT "\n", graph->subset_ncc[graph->subset[i] - 1]));
    }
  }
  PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "Total number of connected components %" PetscInt_FMT "\n", graph->ncc));
  PetscCall(PetscMalloc1(graph->cptr[graph->ncc], &queue_in_global_numbering));
  PetscCall(ISLocalToGlobalMappingApply(graph->l2gmap, graph->cptr[graph->ncc], graph->queue, queue_in_global_numbering));
  for (i = 0; i < graph->ncc; i++) {
    PetscInt  node_num = graph->queue[graph->cptr[i]];
    PetscBool printcc  = PETSC_FALSE;
    PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "  cc %" PetscInt_FMT " (size %" PetscInt_FMT ", fid %" PetscInt_FMT ", neighs:", i, graph->cptr[i + 1] - graph->cptr[i], graph->which_dof[node_num]));
    PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
    for (j = 0; j < graph->count[node_num]; j++) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %" PetscInt_FMT, graph->neighbours_set[node_num][j]));
    if (verbosity_level > 1) {
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "):"));
      if (verbosity_level > 2 || graph->twodim || graph->count[node_num] > 1 || (graph->count[node_num] == 1 && graph->special_dof[node_num] == PCBDDCGRAPH_NEUMANN_MARK)) printcc = PETSC_TRUE;
      if (printcc) {
        for (j = graph->cptr[i]; j < graph->cptr[i + 1]; j++) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %" PetscInt_FMT " (%" PetscInt_FMT ")", graph->queue[j], queue_in_global_numbering[j]));
      }
    } else {
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, ")"));
    }
    PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\n"));
    PetscCall(PetscViewerASCIISetTab(viewer, tabs));
    PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
  }
  PetscCall(PetscFree(queue_in_global_numbering));
  PetscCall(PetscViewerFlush(viewer));
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphRestoreCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS) {
  PetscInt       i;
  PetscContainer gcand;

  PetscFunctionBegin;
  PetscCall(PetscObjectQuery((PetscObject)graph->l2gmap, "_PCBDDCGraphCandidatesIS", (PetscObject *)&gcand));
  if (gcand) {
    if (n_faces) *n_faces = 0;
    if (n_edges) *n_edges = 0;
    if (FacesIS) *FacesIS = NULL;
    if (EdgesIS) *EdgesIS = NULL;
    if (VerticesIS) *VerticesIS = NULL;
  }
  if (n_faces) {
    if (FacesIS) {
      for (i = 0; i < *n_faces; i++) PetscCall(ISDestroy(&((*FacesIS)[i])));
      PetscCall(PetscFree(*FacesIS));
    }
    *n_faces = 0;
  }
  if (n_edges) {
    if (EdgesIS) {
      for (i = 0; i < *n_edges; i++) PetscCall(ISDestroy(&((*EdgesIS)[i])));
      PetscCall(PetscFree(*EdgesIS));
    }
    *n_edges = 0;
  }
  if (VerticesIS) PetscCall(ISDestroy(VerticesIS));
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphGetCandidatesIS(PCBDDCGraph graph, PetscInt *n_faces, IS *FacesIS[], PetscInt *n_edges, IS *EdgesIS[], IS *VerticesIS) {
  IS            *ISForFaces, *ISForEdges, ISForVertices;
  PetscInt       i, nfc, nec, nvc, *idx, *mark;
  PetscContainer gcand;

  PetscFunctionBegin;
  PetscCall(PetscObjectQuery((PetscObject)graph->l2gmap, "_PCBDDCGraphCandidatesIS", (PetscObject *)&gcand));
  if (gcand) {
    PCBDDCGraphCandidates cand;

    PetscCall(PetscContainerGetPointer(gcand, (void **)&cand));
    if (n_faces) *n_faces = cand->nfc;
    if (FacesIS) *FacesIS = cand->Faces;
    if (n_edges) *n_edges = cand->nec;
    if (EdgesIS) *EdgesIS = cand->Edges;
    if (VerticesIS) *VerticesIS = cand->Vertices;
    PetscFunctionReturn(0);
  }
  PetscCall(PetscCalloc1(graph->ncc, &mark));
  /* loop on ccs to evalute number of faces, edges and vertices */
  nfc = 0;
  nec = 0;
  nvc = 0;
  for (i = 0; i < graph->ncc; i++) {
    PetscInt repdof = graph->queue[graph->cptr[i]];
    if (graph->cptr[i + 1] - graph->cptr[i] > graph->custom_minimal_size && graph->count[repdof] < graph->maxcount) {
      if (!graph->twodim && graph->count[repdof] == 1 && graph->special_dof[repdof] != PCBDDCGRAPH_NEUMANN_MARK) {
        nfc++;
        mark[i] = 2;
      } else {
        nec++;
        mark[i] = 1;
      }
    } else {
      nvc += graph->cptr[i + 1] - graph->cptr[i];
    }
  }

  /* allocate IS arrays for faces, edges. Vertices need a single index set. */
  if (FacesIS) PetscCall(PetscMalloc1(nfc, &ISForFaces));
  if (EdgesIS) PetscCall(PetscMalloc1(nec, &ISForEdges));
  if (VerticesIS) PetscCall(PetscMalloc1(nvc, &idx));

  /* loop on ccs to compute index sets for faces and edges */
  if (!graph->queue_sorted) {
    PetscInt *queue_global;

    PetscCall(PetscMalloc1(graph->cptr[graph->ncc], &queue_global));
    PetscCall(ISLocalToGlobalMappingApply(graph->l2gmap, graph->cptr[graph->ncc], graph->queue, queue_global));
    for (i = 0; i < graph->ncc; i++) PetscCall(PetscSortIntWithArray(graph->cptr[i + 1] - graph->cptr[i], &queue_global[graph->cptr[i]], &graph->queue[graph->cptr[i]]));
    PetscCall(PetscFree(queue_global));
    graph->queue_sorted = PETSC_TRUE;
  }
  nfc = 0;
  nec = 0;
  for (i = 0; i < graph->ncc; i++) {
    if (mark[i] == 2) {
      if (FacesIS) PetscCall(ISCreateGeneral(PETSC_COMM_SELF, graph->cptr[i + 1] - graph->cptr[i], &graph->queue[graph->cptr[i]], PETSC_USE_POINTER, &ISForFaces[nfc]));
      nfc++;
    } else if (mark[i] == 1) {
      if (EdgesIS) PetscCall(ISCreateGeneral(PETSC_COMM_SELF, graph->cptr[i + 1] - graph->cptr[i], &graph->queue[graph->cptr[i]], PETSC_USE_POINTER, &ISForEdges[nec]));
      nec++;
    }
  }

  /* index set for vertices */
  if (VerticesIS) {
    nvc = 0;
    for (i = 0; i < graph->ncc; i++) {
      if (!mark[i]) {
        PetscInt j;

        for (j = graph->cptr[i]; j < graph->cptr[i + 1]; j++) {
          idx[nvc] = graph->queue[j];
          nvc++;
        }
      }
    }
    /* sort vertex set (by local ordering) */
    PetscCall(PetscSortInt(nvc, idx));
    PetscCall(ISCreateGeneral(PETSC_COMM_SELF, nvc, idx, PETSC_OWN_POINTER, &ISForVertices));
  }
  PetscCall(PetscFree(mark));

  /* get back info */
  if (n_faces) *n_faces = nfc;
  if (FacesIS) *FacesIS = ISForFaces;
  if (n_edges) *n_edges = nec;
  if (EdgesIS) *EdgesIS = ISForEdges;
  if (VerticesIS) *VerticesIS = ISForVertices;
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphComputeConnectedComponents(PCBDDCGraph graph) {
  PetscBool   adapt_interface_reduced;
  MPI_Comm    interface_comm;
  PetscMPIInt size;
  PetscInt    i;
  PetscBT     cornerp;

  PetscFunctionBegin;
  /* compute connected components locally */
  PetscCall(PetscObjectGetComm((PetscObject)(graph->l2gmap), &interface_comm));
  PetscCall(PCBDDCGraphComputeConnectedComponentsLocal(graph));

  cornerp = NULL;
  if (graph->active_coords) { /* face based corner selection */
    PetscBT    excluded;
    PetscReal *wdist;
    PetscInt   n_neigh, *neigh, *n_shared, **shared;
    PetscInt   maxc, ns;

    PetscCall(PetscBTCreate(graph->nvtxs, &cornerp));
    PetscCall(ISLocalToGlobalMappingGetInfo(graph->l2gmap, &n_neigh, &neigh, &n_shared, &shared));
    for (ns = 1, maxc = 0; ns < n_neigh; ns++) maxc = PetscMax(maxc, n_shared[ns]);
    PetscCall(PetscMalloc1(maxc * graph->cdim, &wdist));
    PetscCall(PetscBTCreate(maxc, &excluded));

    for (ns = 1; ns < n_neigh; ns++) { /* first proc is self */
      PetscReal *anchor, mdist;
      PetscInt   fst, j, k, d, cdim = graph->cdim, n = n_shared[ns];
      PetscInt   point1, point2, point3, point4;

      /* import coordinates on shared interface */
      PetscCall(PetscBTMemzero(n, excluded));
      for (j = 0, fst = -1, k = 0; j < n; j++) {
        PetscBool skip = PETSC_FALSE;
        for (d = 0; d < cdim; d++) {
          PetscReal c = graph->coords[shared[ns][j] * cdim + d];
          skip        = (PetscBool)(skip || c == PETSC_MAX_REAL);
          wdist[k++]  = c;
        }
        if (skip) {
          PetscCall(PetscBTSet(excluded, j));
        } else if (fst == -1) fst = j;
      }
      if (fst == -1) continue;

      /* the dofs are sorted by global numbering, so each rank starts from the same id
         and it will detect the same corners from the given set */

      /* find the farthest point from the starting one */
      anchor = wdist + fst * cdim;
      mdist  = -1.0;
      point1 = fst;
      for (j = fst; j < n; j++) {
        PetscReal dist = 0.0;

        if (PetscUnlikely(PetscBTLookup(excluded, j))) continue;
        for (d = 0; d < cdim; d++) dist += (wdist[j * cdim + d] - anchor[d]) * (wdist[j * cdim + d] - anchor[d]);
        if (dist > mdist) {
          mdist  = dist;
          point1 = j;
        }
      }

      /* find the farthest point from point1 */
      anchor = wdist + point1 * cdim;
      mdist  = -1.0;
      point2 = point1;
      for (j = fst; j < n; j++) {
        PetscReal dist = 0.0;

        if (PetscUnlikely(PetscBTLookup(excluded, j))) continue;
        for (d = 0; d < cdim; d++) dist += (wdist[j * cdim + d] - anchor[d]) * (wdist[j * cdim + d] - anchor[d]);
        if (dist > mdist) {
          mdist  = dist;
          point2 = j;
        }
      }

      /* find the third point maximizing the triangle area */
      point3 = point2;
      if (cdim > 2) {
        PetscReal a = 0.0;

        for (d = 0; d < cdim; d++) a += (wdist[point1 * cdim + d] - wdist[point2 * cdim + d]) * (wdist[point1 * cdim + d] - wdist[point2 * cdim + d]);
        a     = PetscSqrtReal(a);
        mdist = -1.0;
        for (j = fst; j < n; j++) {
          PetscReal area, b = 0.0, c = 0.0, s;

          if (PetscUnlikely(PetscBTLookup(excluded, j))) continue;
          for (d = 0; d < cdim; d++) {
            b += (wdist[point1 * cdim + d] - wdist[j * cdim + d]) * (wdist[point1 * cdim + d] - wdist[j * cdim + d]);
            c += (wdist[point2 * cdim + d] - wdist[j * cdim + d]) * (wdist[point2 * cdim + d] - wdist[j * cdim + d]);
          }
          b = PetscSqrtReal(b);
          c = PetscSqrtReal(c);
          s = 0.5 * (a + b + c);

          /* Heron's formula, area squared */
          area = s * (s - a) * (s - b) * (s - c);
          if (area > mdist) {
            mdist  = area;
            point3 = j;
          }
        }
      }

      /* find the farthest point from point3 different from point1 and point2 */
      anchor = wdist + point3 * cdim;
      mdist  = -1.0;
      point4 = point3;
      for (j = fst; j < n; j++) {
        PetscReal dist = 0.0;

        if (PetscUnlikely(PetscBTLookup(excluded, j)) || j == point1 || j == point2 || j == point3) continue;
        for (d = 0; d < cdim; d++) dist += (wdist[j * cdim + d] - anchor[d]) * (wdist[j * cdim + d] - anchor[d]);
        if (dist > mdist) {
          mdist  = dist;
          point4 = j;
        }
      }

      PetscCall(PetscBTSet(cornerp, shared[ns][point1]));
      PetscCall(PetscBTSet(cornerp, shared[ns][point2]));
      PetscCall(PetscBTSet(cornerp, shared[ns][point3]));
      PetscCall(PetscBTSet(cornerp, shared[ns][point4]));

      /* all dofs having the same coordinates will be primal */
      for (j = fst; j < n; j++) {
        PetscBool same[] = {PETSC_TRUE, PETSC_TRUE, PETSC_TRUE, PETSC_TRUE};

        if (PetscUnlikely(PetscBTLookup(excluded, j))) continue;
        for (d = 0; d < cdim; d++) {
          same[0] = (PetscBool)(same[0] && (PetscAbsReal(wdist[j * cdim + d] - wdist[point1 * cdim + d]) < PETSC_SMALL));
          same[1] = (PetscBool)(same[1] && (PetscAbsReal(wdist[j * cdim + d] - wdist[point2 * cdim + d]) < PETSC_SMALL));
          same[2] = (PetscBool)(same[2] && (PetscAbsReal(wdist[j * cdim + d] - wdist[point3 * cdim + d]) < PETSC_SMALL));
          same[3] = (PetscBool)(same[3] && (PetscAbsReal(wdist[j * cdim + d] - wdist[point4 * cdim + d]) < PETSC_SMALL));
        }
        if (same[0] || same[1] || same[2] || same[3]) PetscCall(PetscBTSet(cornerp, shared[ns][j]));
      }
    }
    PetscCall(PetscBTDestroy(&excluded));
    PetscCall(PetscFree(wdist));
    PetscCall(ISLocalToGlobalMappingRestoreInfo(graph->l2gmap, &n_neigh, &neigh, &n_shared, &shared));
  }

  /* check consistency of connected components among neighbouring subdomains -> it adapt them in case it is needed */
  PetscCallMPI(MPI_Comm_size(interface_comm, &size));
  adapt_interface_reduced = PETSC_FALSE;
  if (size > 1) {
    PetscInt  i;
    PetscBool adapt_interface = cornerp ? PETSC_TRUE : PETSC_FALSE;
    for (i = 0; i < graph->n_subsets && !adapt_interface; i++) {
      /* We are not sure that on a given subset of the local interface,
         with two connected components, the latters be the same among sharing subdomains */
      if (graph->subset_ncc[i] > 1) adapt_interface = PETSC_TRUE;
    }
    PetscCall(MPIU_Allreduce(&adapt_interface, &adapt_interface_reduced, 1, MPIU_BOOL, MPI_LOR, interface_comm));
  }

  if (graph->n_subsets && adapt_interface_reduced) {
    PetscBT      subset_cc_adapt;
    MPI_Request *send_requests, *recv_requests;
    PetscInt    *send_buffer, *recv_buffer;
    PetscInt     sum_requests, start_of_recv, start_of_send;
    PetscInt    *cum_recv_counts;
    PetscInt    *labels;
    PetscInt     ncc, cum_queue, mss, mns, j, k, s;
    PetscInt   **refine_buffer = NULL, *private_labels = NULL;
    PetscBool   *subset_has_corn, *recv_buffer_bool, *send_buffer_bool;

    PetscCall(PetscCalloc1(graph->n_subsets, &subset_has_corn));
    if (cornerp) {
      for (i = 0; i < graph->n_subsets; i++) {
        for (j = 0; j < graph->subset_size[i]; j++) {
          if (PetscBTLookup(cornerp, graph->subset_idxs[i][j])) {
            subset_has_corn[i] = PETSC_TRUE;
            break;
          }
        }
      }
    }
    PetscCall(PetscMalloc1(graph->nvtxs, &labels));
    PetscCall(PetscArrayzero(labels, graph->nvtxs));
    for (i = 0, k = 0; i < graph->ncc; i++) {
      PetscInt s = 1;
      for (j = graph->cptr[i]; j < graph->cptr[i + 1]; j++) {
        if (cornerp && PetscBTLookup(cornerp, graph->queue[j])) {
          labels[graph->queue[j]] = k + s;
          s += 1;
        } else {
          labels[graph->queue[j]] = k;
        }
      }
      k += s;
    }

    /* allocate some space */
    PetscCall(PetscMalloc1(graph->n_subsets + 1, &cum_recv_counts));
    PetscCall(PetscArrayzero(cum_recv_counts, graph->n_subsets + 1));

    /* first count how many neighbours per connected component I will receive from */
    cum_recv_counts[0] = 0;
    for (i = 0; i < graph->n_subsets; i++) cum_recv_counts[i + 1] = cum_recv_counts[i] + graph->count[graph->subset_idxs[i][0]];
    PetscCall(PetscMalloc1(graph->n_subsets, &send_buffer_bool));
    PetscCall(PetscMalloc1(cum_recv_counts[graph->n_subsets], &recv_buffer_bool));
    PetscCall(PetscMalloc2(cum_recv_counts[graph->n_subsets], &send_requests, cum_recv_counts[graph->n_subsets], &recv_requests));
    for (i = 0; i < cum_recv_counts[graph->n_subsets]; i++) {
      send_requests[i] = MPI_REQUEST_NULL;
      recv_requests[i] = MPI_REQUEST_NULL;
    }

    /* exchange with my neighbours the number of my connected components on the subset of interface */
    sum_requests = 0;
    for (i = 0; i < graph->n_subsets; i++) send_buffer_bool[i] = (PetscBool)(graph->subset_ncc[i] > 1 || subset_has_corn[i]);
    for (i = 0; i < graph->n_subsets; i++) {
      PetscMPIInt neigh, tag;
      PetscInt    count, *neighs;

      count  = graph->count[graph->subset_idxs[i][0]];
      neighs = graph->neighbours_set[graph->subset_idxs[i][0]];
      PetscCall(PetscMPIIntCast(2 * graph->subset_ref_node[i], &tag));
      for (k = 0; k < count; k++) {
        PetscCall(PetscMPIIntCast(neighs[k], &neigh));
        PetscCallMPI(MPI_Isend(send_buffer_bool + i, 1, MPIU_BOOL, neigh, tag, interface_comm, &send_requests[sum_requests]));
        PetscCallMPI(MPI_Irecv(recv_buffer_bool + sum_requests, 1, MPIU_BOOL, neigh, tag, interface_comm, &recv_requests[sum_requests]));
        sum_requests++;
      }
    }
    PetscCallMPI(MPI_Waitall(sum_requests, recv_requests, MPI_STATUSES_IGNORE));
    PetscCallMPI(MPI_Waitall(sum_requests, send_requests, MPI_STATUSES_IGNORE));

    /* determine the subsets I have to adapt (those having more than 1 cc) */
    PetscCall(PetscBTCreate(graph->n_subsets, &subset_cc_adapt));
    PetscCall(PetscBTMemzero(graph->n_subsets, subset_cc_adapt));
    for (i = 0; i < graph->n_subsets; i++) {
      if (graph->subset_ncc[i] > 1 || subset_has_corn[i]) {
        PetscCall(PetscBTSet(subset_cc_adapt, i));
        continue;
      }
      for (j = cum_recv_counts[i]; j < cum_recv_counts[i + 1]; j++) {
        if (recv_buffer_bool[j]) {
          PetscCall(PetscBTSet(subset_cc_adapt, i));
          break;
        }
      }
    }
    PetscCall(PetscFree(send_buffer_bool));
    PetscCall(PetscFree(recv_buffer_bool));
    PetscCall(PetscFree(subset_has_corn));

    /* determine send/recv buffers sizes */
    j   = 0;
    mss = 0;
    for (i = 0; i < graph->n_subsets; i++) {
      if (PetscBTLookup(subset_cc_adapt, i)) {
        j += graph->subset_size[i];
        mss = PetscMax(graph->subset_size[i], mss);
      }
    }
    k   = 0;
    mns = 0;
    for (i = 0; i < graph->n_subsets; i++) {
      if (PetscBTLookup(subset_cc_adapt, i)) {
        k += (cum_recv_counts[i + 1] - cum_recv_counts[i]) * graph->subset_size[i];
        mns = PetscMax(cum_recv_counts[i + 1] - cum_recv_counts[i], mns);
      }
    }
    PetscCall(PetscMalloc2(j, &send_buffer, k, &recv_buffer));

    /* fill send buffer (order matters: subset_idxs ordered by global ordering) */
    j = 0;
    for (i = 0; i < graph->n_subsets; i++)
      if (PetscBTLookup(subset_cc_adapt, i))
        for (k = 0; k < graph->subset_size[i]; k++) send_buffer[j++] = labels[graph->subset_idxs[i][k]];

    /* now exchange the data */
    start_of_recv = 0;
    start_of_send = 0;
    sum_requests  = 0;
    for (i = 0; i < graph->n_subsets; i++) {
      if (PetscBTLookup(subset_cc_adapt, i)) {
        PetscMPIInt neigh, tag;
        PetscInt    size_of_send = graph->subset_size[i];

        j = graph->subset_idxs[i][0];
        PetscCall(PetscMPIIntCast(2 * graph->subset_ref_node[i] + 1, &tag));
        for (k = 0; k < graph->count[j]; k++) {
          PetscCall(PetscMPIIntCast(graph->neighbours_set[j][k], &neigh));
          PetscCallMPI(MPI_Isend(&send_buffer[start_of_send], size_of_send, MPIU_INT, neigh, tag, interface_comm, &send_requests[sum_requests]));
          PetscCallMPI(MPI_Irecv(&recv_buffer[start_of_recv], size_of_send, MPIU_INT, neigh, tag, interface_comm, &recv_requests[sum_requests]));
          start_of_recv += size_of_send;
          sum_requests++;
        }
        start_of_send += size_of_send;
      }
    }
    PetscCallMPI(MPI_Waitall(sum_requests, recv_requests, MPI_STATUSES_IGNORE));

    /* refine connected components */
    start_of_recv = 0;
    /* allocate some temporary space */
    if (mss) {
      PetscCall(PetscMalloc1(mss, &refine_buffer));
      PetscCall(PetscMalloc2(mss * (mns + 1), &refine_buffer[0], mss, &private_labels));
    }
    ncc            = 0;
    cum_queue      = 0;
    graph->cptr[0] = 0;
    for (i = 0; i < graph->n_subsets; i++) {
      if (PetscBTLookup(subset_cc_adapt, i)) {
        PetscInt subset_counter = 0;
        PetscInt sharingprocs   = cum_recv_counts[i + 1] - cum_recv_counts[i] + 1; /* count myself */
        PetscInt buffer_size    = graph->subset_size[i];

        /* compute pointers */
        for (j = 1; j < buffer_size; j++) refine_buffer[j] = refine_buffer[j - 1] + sharingprocs;
        /* analyze contributions from subdomains that share the i-th subset
           The structure of refine_buffer is suitable to find intersections of ccs among sharingprocs.
           supposing the current subset is shared by 3 processes and has dimension 5 with global dofs 0,1,2,3,4 (local 0,4,3,1,2)
           sharing procs connected components:
             neigh 0: [0 1 4], [2 3], labels [4,7]  (2 connected components)
             neigh 1: [0 1], [2 3 4], labels [3 2]  (2 connected components)
             neigh 2: [0 4], [1], [2 3], labels [1 5 6] (3 connected components)
           refine_buffer will be filled as:
             [ 4, 3, 1;
               4, 2, 1;
               7, 2, 6;
               4, 3, 5;
               7, 2, 6; ];
           The connected components in local ordering are [0], [1], [2 3], [4] */
        /* fill temp_buffer */
        for (k = 0; k < buffer_size; k++) refine_buffer[k][0] = labels[graph->subset_idxs[i][k]];
        for (j = 0; j < sharingprocs - 1; j++) {
          for (k = 0; k < buffer_size; k++) refine_buffer[k][j + 1] = recv_buffer[start_of_recv + k];
          start_of_recv += buffer_size;
        }
        PetscCall(PetscArrayzero(private_labels, buffer_size));
        for (j = 0; j < buffer_size; j++) {
          if (!private_labels[j]) { /* found a new cc  */
            PetscBool same_set;

            graph->cptr[ncc] = cum_queue;
            ncc++;
            subset_counter++;
            private_labels[j]         = subset_counter;
            graph->queue[cum_queue++] = graph->subset_idxs[i][j];
            for (k = j + 1; k < buffer_size; k++) { /* check for other nodes in new cc */
              same_set = PETSC_TRUE;
              for (s = 0; s < sharingprocs; s++) {
                if (refine_buffer[j][s] != refine_buffer[k][s]) {
                  same_set = PETSC_FALSE;
                  break;
                }
              }
              if (same_set) {
                private_labels[k]         = subset_counter;
                graph->queue[cum_queue++] = graph->subset_idxs[i][k];
              }
            }
          }
        }
        graph->cptr[ncc]     = cum_queue;
        graph->subset_ncc[i] = subset_counter;
        graph->queue_sorted  = PETSC_FALSE;
      } else { /* this subset does not need to be adapted */
        PetscCall(PetscArraycpy(graph->queue + cum_queue, graph->subset_idxs[i], graph->subset_size[i]));
        ncc++;
        cum_queue += graph->subset_size[i];
        graph->cptr[ncc] = cum_queue;
      }
    }
    graph->cptr[ncc] = cum_queue;
    graph->ncc       = ncc;
    if (mss) {
      PetscCall(PetscFree2(refine_buffer[0], private_labels));
      PetscCall(PetscFree(refine_buffer));
    }
    PetscCall(PetscFree(labels));
    PetscCallMPI(MPI_Waitall(sum_requests, send_requests, MPI_STATUSES_IGNORE));
    PetscCall(PetscFree2(send_requests, recv_requests));
    PetscCall(PetscFree2(send_buffer, recv_buffer));
    PetscCall(PetscFree(cum_recv_counts));
    PetscCall(PetscBTDestroy(&subset_cc_adapt));
  }
  PetscCall(PetscBTDestroy(&cornerp));

  /* Determine if we are in 2D or 3D */
  if (!graph->twodimset) {
    PetscBool twodim = PETSC_TRUE;
    for (i = 0; i < graph->ncc; i++) {
      PetscInt repdof = graph->queue[graph->cptr[i]];
      PetscInt ccsize = graph->cptr[i + 1] - graph->cptr[i];
      if (graph->count[repdof] > 1 && ccsize > graph->custom_minimal_size) {
        twodim = PETSC_FALSE;
        break;
      }
    }
    PetscCall(MPIU_Allreduce(&twodim, &graph->twodim, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)graph->l2gmap)));
    graph->twodimset = PETSC_TRUE;
  }
  PetscFunctionReturn(0);
}

static inline PetscErrorCode PCBDDCGraphComputeCC_Private(PCBDDCGraph graph, PetscInt pid, PetscInt *queue_tip, PetscInt n_prev, PetscInt *n_added) {
  PetscInt  i, j, n;
  PetscInt *xadj = graph->xadj, *adjncy = graph->adjncy;
  PetscBT   touched  = graph->touched;
  PetscBool havecsr  = (PetscBool)(!!xadj);
  PetscBool havesubs = (PetscBool)(!!graph->n_local_subs);

  PetscFunctionBegin;
  n = 0;
  if (havecsr && !havesubs) {
    for (i = -n_prev; i < 0; i++) {
      PetscInt start_dof = queue_tip[i];
      /* we assume that if a dof has a size 1 adjacency list and the corresponding entry is negative, it is connected to all dofs */
      if (xadj[start_dof + 1] - xadj[start_dof] == 1 && adjncy[xadj[start_dof]] < 0) {
        for (j = 0; j < graph->subset_size[pid - 1]; j++) { /* pid \in [1,graph->n_subsets] */
          PetscInt dof = graph->subset_idxs[pid - 1][j];
          if (!PetscBTLookup(touched, dof) && graph->subset[dof] == pid) {
            PetscCall(PetscBTSet(touched, dof));
            queue_tip[n] = dof;
            n++;
          }
        }
      } else {
        for (j = xadj[start_dof]; j < xadj[start_dof + 1]; j++) {
          PetscInt dof = adjncy[j];
          if (!PetscBTLookup(touched, dof) && graph->subset[dof] == pid) {
            PetscCall(PetscBTSet(touched, dof));
            queue_tip[n] = dof;
            n++;
          }
        }
      }
    }
  } else if (havecsr && havesubs) {
    PetscInt sid = graph->local_subs[queue_tip[-n_prev]];
    for (i = -n_prev; i < 0; i++) {
      PetscInt start_dof = queue_tip[i];
      /* we assume that if a dof has a size 1 adjacency list and the corresponding entry is negative, it is connected to all dofs belonging to the local sub */
      if (xadj[start_dof + 1] - xadj[start_dof] == 1 && adjncy[xadj[start_dof]] < 0) {
        for (j = 0; j < graph->subset_size[pid - 1]; j++) { /* pid \in [1,graph->n_subsets] */
          PetscInt dof = graph->subset_idxs[pid - 1][j];
          if (!PetscBTLookup(touched, dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
            PetscCall(PetscBTSet(touched, dof));
            queue_tip[n] = dof;
            n++;
          }
        }
      } else {
        for (j = xadj[start_dof]; j < xadj[start_dof + 1]; j++) {
          PetscInt dof = adjncy[j];
          if (!PetscBTLookup(touched, dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
            PetscCall(PetscBTSet(touched, dof));
            queue_tip[n] = dof;
            n++;
          }
        }
      }
    }
  } else if (havesubs) { /* sub info only */
    PetscInt sid = graph->local_subs[queue_tip[-n_prev]];
    for (j = 0; j < graph->subset_size[pid - 1]; j++) { /* pid \in [1,graph->n_subsets] */
      PetscInt dof = graph->subset_idxs[pid - 1][j];
      if (!PetscBTLookup(touched, dof) && graph->subset[dof] == pid && graph->local_subs[dof] == sid) {
        PetscCall(PetscBTSet(touched, dof));
        queue_tip[n] = dof;
        n++;
      }
    }
  } else {
    for (j = 0; j < graph->subset_size[pid - 1]; j++) { /* pid \in [1,graph->n_subsets] */
      PetscInt dof = graph->subset_idxs[pid - 1][j];
      if (!PetscBTLookup(touched, dof) && graph->subset[dof] == pid) {
        PetscCall(PetscBTSet(touched, dof));
        queue_tip[n] = dof;
        n++;
      }
    }
  }
  *n_added = n;
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphComputeConnectedComponentsLocal(PCBDDCGraph graph) {
  PetscInt    ncc, cum_queue, n;
  PetscMPIInt commsize;

  PetscFunctionBegin;
  PetscCheck(graph->setupcalled, PetscObjectComm((PetscObject)graph->l2gmap), PETSC_ERR_ORDER, "PCBDDCGraphSetUp should be called first");
  /* quiet return if there isn't any local info */
  if (!graph->xadj && !graph->n_local_subs) PetscFunctionReturn(0);

  /* reset any previous search of connected components */
  PetscCall(PetscBTMemzero(graph->nvtxs, graph->touched));
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)graph->l2gmap), &commsize));
  if (commsize > graph->commsizelimit) {
    PetscInt i;
    for (i = 0; i < graph->nvtxs; i++) {
      if (graph->special_dof[i] == PCBDDCGRAPH_DIRICHLET_MARK || !graph->count[i]) PetscCall(PetscBTSet(graph->touched, i));
    }
  }

  /* begin search for connected components */
  cum_queue = 0;
  ncc       = 0;
  for (n = 0; n < graph->n_subsets; n++) {
    PetscInt pid   = n + 1; /* partition labeled by 0 is discarded */
    PetscInt found = 0, prev = 0, first = 0, ncc_pid = 0;
    while (found != graph->subset_size[n]) {
      PetscInt added = 0;
      if (!prev) { /* search for new starting dof */
        while (PetscBTLookup(graph->touched, graph->subset_idxs[n][first])) first++;
        PetscCall(PetscBTSet(graph->touched, graph->subset_idxs[n][first]));
        graph->queue[cum_queue] = graph->subset_idxs[n][first];
        graph->cptr[ncc]        = cum_queue;
        prev                    = 1;
        cum_queue++;
        found++;
        ncc_pid++;
        ncc++;
      }
      PetscCall(PCBDDCGraphComputeCC_Private(graph, pid, graph->queue + cum_queue, prev, &added));
      if (!added) {
        graph->subset_ncc[n] = ncc_pid;
        graph->cptr[ncc]     = cum_queue;
      }
      prev = added;
      found += added;
      cum_queue += added;
      if (added && found == graph->subset_size[n]) {
        graph->subset_ncc[n] = ncc_pid;
        graph->cptr[ncc]     = cum_queue;
      }
    }
  }
  graph->ncc          = ncc;
  graph->queue_sorted = PETSC_FALSE;
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphSetUp(PCBDDCGraph graph, PetscInt custom_minimal_size, IS neumann_is, IS dirichlet_is, PetscInt n_ISForDofs, IS ISForDofs[], IS custom_primal_vertices) {
  IS              subset, subset_n;
  MPI_Comm        comm;
  const PetscInt *is_indices;
  PetscInt        n_neigh, *neigh, *n_shared, **shared, *queue_global;
  PetscInt        i, j, k, s, total_counts, nodes_touched, is_size;
  PetscMPIInt     commsize;
  PetscBool       same_set, mirrors_found;

  PetscFunctionBegin;
  PetscValidLogicalCollectiveInt(graph->l2gmap, custom_minimal_size, 2);
  if (neumann_is) {
    PetscValidHeaderSpecific(neumann_is, IS_CLASSID, 3);
    PetscCheckSameComm(graph->l2gmap, 1, neumann_is, 3);
  }
  graph->has_dirichlet = PETSC_FALSE;
  if (dirichlet_is) {
    PetscValidHeaderSpecific(dirichlet_is, IS_CLASSID, 4);
    PetscCheckSameComm(graph->l2gmap, 1, dirichlet_is, 4);
    graph->has_dirichlet = PETSC_TRUE;
  }
  PetscValidLogicalCollectiveInt(graph->l2gmap, n_ISForDofs, 5);
  for (i = 0; i < n_ISForDofs; i++) {
    PetscValidHeaderSpecific(ISForDofs[i], IS_CLASSID, 6);
    PetscCheckSameComm(graph->l2gmap, 1, ISForDofs[i], 6);
  }
  if (custom_primal_vertices) {
    PetscValidHeaderSpecific(custom_primal_vertices, IS_CLASSID, 7);
    PetscCheckSameComm(graph->l2gmap, 1, custom_primal_vertices, 7);
  }
  PetscCall(PetscObjectGetComm((PetscObject)(graph->l2gmap), &comm));
  PetscCallMPI(MPI_Comm_size(comm, &commsize));

  /* custom_minimal_size */
  graph->custom_minimal_size = custom_minimal_size;
  /* get info l2gmap and allocate work vectors  */
  PetscCall(ISLocalToGlobalMappingGetInfo(graph->l2gmap, &n_neigh, &neigh, &n_shared, &shared));
  /* check if we have any local periodic nodes (periodic BCs) */
  mirrors_found = PETSC_FALSE;
  if (graph->nvtxs && n_neigh) {
    for (i = 0; i < n_shared[0]; i++) graph->count[shared[0][i]] += 1;
    for (i = 0; i < n_shared[0]; i++) {
      if (graph->count[shared[0][i]] > 1) {
        mirrors_found = PETSC_TRUE;
        break;
      }
    }
  }
  /* compute local mirrors (if any) */
  if (mirrors_found) {
    IS        to, from;
    PetscInt *local_indices, *global_indices;

    PetscCall(ISCreateStride(PETSC_COMM_SELF, graph->nvtxs, 0, 1, &to));
    PetscCall(ISLocalToGlobalMappingApplyIS(graph->l2gmap, to, &from));
    /* get arrays of local and global indices */
    PetscCall(PetscMalloc1(graph->nvtxs, &local_indices));
    PetscCall(ISGetIndices(to, (const PetscInt **)&is_indices));
    PetscCall(PetscArraycpy(local_indices, is_indices, graph->nvtxs));
    PetscCall(ISRestoreIndices(to, (const PetscInt **)&is_indices));
    PetscCall(PetscMalloc1(graph->nvtxs, &global_indices));
    PetscCall(ISGetIndices(from, (const PetscInt **)&is_indices));
    PetscCall(PetscArraycpy(global_indices, is_indices, graph->nvtxs));
    PetscCall(ISRestoreIndices(from, (const PetscInt **)&is_indices));
    /* allocate space for mirrors */
    PetscCall(PetscMalloc2(graph->nvtxs, &graph->mirrors, graph->nvtxs, &graph->mirrors_set));
    PetscCall(PetscArrayzero(graph->mirrors, graph->nvtxs));
    graph->mirrors_set[0] = NULL;

    k = 0;
    for (i = 0; i < n_shared[0]; i++) {
      j = shared[0][i];
      if (graph->count[j] > 1) {
        graph->mirrors[j]++;
        k++;
      }
    }
    /* allocate space for set of mirrors */
    PetscCall(PetscMalloc1(k, &graph->mirrors_set[0]));
    for (i = 1; i < graph->nvtxs; i++) graph->mirrors_set[i] = graph->mirrors_set[i - 1] + graph->mirrors[i - 1];

    /* fill arrays */
    PetscCall(PetscArrayzero(graph->mirrors, graph->nvtxs));
    for (j = 0; j < n_shared[0]; j++) {
      i = shared[0][j];
      if (graph->count[i] > 1) graph->mirrors_set[i][graph->mirrors[i]++] = global_indices[i];
    }
    PetscCall(PetscSortIntWithArray(graph->nvtxs, global_indices, local_indices));
    for (i = 0; i < graph->nvtxs; i++) {
      if (graph->mirrors[i] > 0) {
        PetscCall(PetscFindInt(graph->mirrors_set[i][0], graph->nvtxs, global_indices, &k));
        j = global_indices[k];
        while (k > 0 && global_indices[k - 1] == j) k--;
        for (j = 0; j < graph->mirrors[i]; j++) graph->mirrors_set[i][j] = local_indices[k + j];
        PetscCall(PetscSortInt(graph->mirrors[i], graph->mirrors_set[i]));
      }
    }
    PetscCall(PetscFree(local_indices));
    PetscCall(PetscFree(global_indices));
    PetscCall(ISDestroy(&to));
    PetscCall(ISDestroy(&from));
  }
  PetscCall(PetscArrayzero(graph->count, graph->nvtxs));

  /* Count total number of neigh per node */
  k = 0;
  for (i = 1; i < n_neigh; i++) {
    k += n_shared[i];
    for (j = 0; j < n_shared[i]; j++) graph->count[shared[i][j]] += 1;
  }
  /* Allocate space for storing the set of neighbours for each node */
  if (graph->nvtxs) PetscCall(PetscMalloc1(k, &graph->neighbours_set[0]));
  for (i = 1; i < graph->nvtxs; i++) { /* dont count myself */
    graph->neighbours_set[i] = graph->neighbours_set[i - 1] + graph->count[i - 1];
  }
  /* Get information for sharing subdomains */
  PetscCall(PetscArrayzero(graph->count, graph->nvtxs));
  for (i = 1; i < n_neigh; i++) { /* dont count myself */
    s = n_shared[i];
    for (j = 0; j < s; j++) {
      k                                         = shared[i][j];
      graph->neighbours_set[k][graph->count[k]] = neigh[i];
      graph->count[k] += 1;
    }
  }
  /* sort set of sharing subdomains */
  for (i = 0; i < graph->nvtxs; i++) PetscCall(PetscSortRemoveDupsInt(&graph->count[i], graph->neighbours_set[i]));
  /* free memory allocated by ISLocalToGlobalMappingGetInfo */
  PetscCall(ISLocalToGlobalMappingRestoreInfo(graph->l2gmap, &n_neigh, &neigh, &n_shared, &shared));

  /*
     Get info for dofs splitting
     User can specify just a subset; an additional field is considered as a complementary field
  */
  for (i = 0, k = 0; i < n_ISForDofs; i++) {
    PetscInt bs;

    PetscCall(ISGetBlockSize(ISForDofs[i], &bs));
    k += bs;
  }
  for (i = 0; i < graph->nvtxs; i++) graph->which_dof[i] = k; /* by default a dof belongs to the complement set */
  for (i = 0, k = 0; i < n_ISForDofs; i++) {
    PetscInt bs;

    PetscCall(ISGetLocalSize(ISForDofs[i], &is_size));
    PetscCall(ISGetBlockSize(ISForDofs[i], &bs));
    PetscCall(ISGetIndices(ISForDofs[i], (const PetscInt **)&is_indices));
    for (j = 0; j < is_size / bs; j++) {
      PetscInt b;

      for (b = 0; b < bs; b++) {
        PetscInt jj = bs * j + b;

        if (is_indices[jj] > -1 && is_indices[jj] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
          graph->which_dof[is_indices[jj]] = k + b;
        }
      }
    }
    PetscCall(ISRestoreIndices(ISForDofs[i], (const PetscInt **)&is_indices));
    k += bs;
  }

  /* Take into account Neumann nodes */
  if (neumann_is) {
    PetscCall(ISGetLocalSize(neumann_is, &is_size));
    PetscCall(ISGetIndices(neumann_is, (const PetscInt **)&is_indices));
    for (i = 0; i < is_size; i++) {
      if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
        graph->special_dof[is_indices[i]] = PCBDDCGRAPH_NEUMANN_MARK;
      }
    }
    PetscCall(ISRestoreIndices(neumann_is, (const PetscInt **)&is_indices));
  }
  /* Take into account Dirichlet nodes (they overwrite any neumann boundary mark previously set) */
  if (dirichlet_is) {
    PetscCall(ISGetLocalSize(dirichlet_is, &is_size));
    PetscCall(ISGetIndices(dirichlet_is, (const PetscInt **)&is_indices));
    for (i = 0; i < is_size; i++) {
      if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs) { /* out of bounds indices (if any) are skipped */
        if (commsize > graph->commsizelimit) {                  /* dirichlet nodes treated as internal */
          PetscCall(PetscBTSet(graph->touched, is_indices[i]));
          graph->subset[is_indices[i]] = 0;
        }
        graph->special_dof[is_indices[i]] = PCBDDCGRAPH_DIRICHLET_MARK;
      }
    }
    PetscCall(ISRestoreIndices(dirichlet_is, (const PetscInt **)&is_indices));
  }
  /* mark local periodic nodes (if any) and adapt CSR graph (if any) */
  if (graph->mirrors) {
    for (i = 0; i < graph->nvtxs; i++)
      if (graph->mirrors[i]) graph->special_dof[i] = PCBDDCGRAPH_LOCAL_PERIODIC_MARK;

    if (graph->xadj) {
      PetscInt *new_xadj, *new_adjncy;
      /* sort CSR graph */
      for (i = 0; i < graph->nvtxs; i++) PetscCall(PetscSortInt(graph->xadj[i + 1] - graph->xadj[i], &graph->adjncy[graph->xadj[i]]));
      /* adapt local CSR graph in case of local periodicity */
      k = 0;
      for (i = 0; i < graph->nvtxs; i++)
        for (j = graph->xadj[i]; j < graph->xadj[i + 1]; j++) k += graph->mirrors[graph->adjncy[j]];

      PetscCall(PetscMalloc1(graph->nvtxs + 1, &new_xadj));
      PetscCall(PetscMalloc1(k + graph->xadj[graph->nvtxs], &new_adjncy));
      new_xadj[0] = 0;
      for (i = 0; i < graph->nvtxs; i++) {
        k = graph->xadj[i + 1] - graph->xadj[i];
        PetscCall(PetscArraycpy(&new_adjncy[new_xadj[i]], &graph->adjncy[graph->xadj[i]], k));
        new_xadj[i + 1] = new_xadj[i] + k;
        for (j = graph->xadj[i]; j < graph->xadj[i + 1]; j++) {
          k = graph->mirrors[graph->adjncy[j]];
          PetscCall(PetscArraycpy(&new_adjncy[new_xadj[i + 1]], graph->mirrors_set[graph->adjncy[j]], k));
          new_xadj[i + 1] += k;
        }
        k = new_xadj[i + 1] - new_xadj[i];
        PetscCall(PetscSortRemoveDupsInt(&k, &new_adjncy[new_xadj[i]]));
        new_xadj[i + 1] = new_xadj[i] + k;
      }
      /* set new CSR into graph */
      PetscCall(PetscFree(graph->xadj));
      PetscCall(PetscFree(graph->adjncy));
      graph->xadj   = new_xadj;
      graph->adjncy = new_adjncy;
    }
  }

  /* mark special nodes (if any) -> each will become a single node equivalence class */
  if (custom_primal_vertices) {
    PetscCall(ISGetLocalSize(custom_primal_vertices, &is_size));
    PetscCall(ISGetIndices(custom_primal_vertices, (const PetscInt **)&is_indices));
    for (i = 0, j = 0; i < is_size; i++) {
      if (is_indices[i] > -1 && is_indices[i] < graph->nvtxs && graph->special_dof[is_indices[i]] != PCBDDCGRAPH_DIRICHLET_MARK) { /* out of bounds indices (if any) are skipped */
        graph->special_dof[is_indices[i]] = PCBDDCGRAPH_SPECIAL_MARK - j;
        j++;
      }
    }
    PetscCall(ISRestoreIndices(custom_primal_vertices, (const PetscInt **)&is_indices));
  }

  /* mark interior nodes (if commsize > graph->commsizelimit) as touched and belonging to partition number 0 */
  if (commsize > graph->commsizelimit) {
    for (i = 0; i < graph->nvtxs; i++) {
      if (!graph->count[i]) {
        PetscCall(PetscBTSet(graph->touched, i));
        graph->subset[i] = 0;
      }
    }
  }

  /* init graph structure and compute default subsets */
  nodes_touched = 0;
  for (i = 0; i < graph->nvtxs; i++) {
    if (PetscBTLookup(graph->touched, i)) nodes_touched++;
  }
  i            = 0;
  graph->ncc   = 0;
  total_counts = 0;

  /* allocated space for queues */
  if (commsize == graph->commsizelimit) {
    PetscCall(PetscMalloc2(graph->nvtxs + 1, &graph->cptr, graph->nvtxs, &graph->queue));
  } else {
    PetscInt nused = graph->nvtxs - nodes_touched;
    PetscCall(PetscMalloc2(nused + 1, &graph->cptr, nused, &graph->queue));
  }

  while (nodes_touched < graph->nvtxs) {
    /*  find first untouched node in local ordering */
    while (PetscBTLookup(graph->touched, i)) i++;
    PetscCall(PetscBTSet(graph->touched, i));
    graph->subset[i]           = graph->ncc + 1;
    graph->cptr[graph->ncc]    = total_counts;
    graph->queue[total_counts] = i;
    total_counts++;
    nodes_touched++;
    /* now find all other nodes having the same set of sharing subdomains */
    for (j = i + 1; j < graph->nvtxs; j++) {
      /* check for same number of sharing subdomains, dof number and same special mark */
      if (!PetscBTLookup(graph->touched, j) && graph->count[i] == graph->count[j] && graph->which_dof[i] == graph->which_dof[j] && graph->special_dof[i] == graph->special_dof[j]) {
        /* check for same set of sharing subdomains */
        same_set = PETSC_TRUE;
        for (k = 0; k < graph->count[j]; k++) {
          if (graph->neighbours_set[i][k] != graph->neighbours_set[j][k]) same_set = PETSC_FALSE;
        }
        /* I have found a friend of mine */
        if (same_set) {
          PetscCall(PetscBTSet(graph->touched, j));
          graph->subset[j] = graph->ncc + 1;
          nodes_touched++;
          graph->queue[total_counts] = j;
          total_counts++;
        }
      }
    }
    graph->ncc++;
  }
  /* set default number of subsets (at this point no info on csr and/or local_subs has been taken into account, so n_subsets = ncc */
  graph->n_subsets = graph->ncc;
  PetscCall(PetscMalloc1(graph->n_subsets, &graph->subset_ncc));
  for (i = 0; i < graph->n_subsets; i++) graph->subset_ncc[i] = 1;
  /* final pointer */
  graph->cptr[graph->ncc] = total_counts;

  /* For consistency reasons (among neighbours), I need to sort (by global ordering) each connected component */
  /* Get a reference node (min index in global ordering) for each subset for tagging messages */
  PetscCall(PetscMalloc1(graph->ncc, &graph->subset_ref_node));
  PetscCall(PetscMalloc1(graph->cptr[graph->ncc], &queue_global));
  PetscCall(ISLocalToGlobalMappingApply(graph->l2gmap, graph->cptr[graph->ncc], graph->queue, queue_global));
  for (j = 0; j < graph->ncc; j++) {
    PetscCall(PetscSortIntWithArray(graph->cptr[j + 1] - graph->cptr[j], &queue_global[graph->cptr[j]], &graph->queue[graph->cptr[j]]));
    graph->subset_ref_node[j] = graph->queue[graph->cptr[j]];
  }
  PetscCall(PetscFree(queue_global));
  graph->queue_sorted = PETSC_TRUE;

  /* save information on subsets (needed when analyzing the connected components) */
  if (graph->ncc) {
    PetscCall(PetscMalloc2(graph->ncc, &graph->subset_size, graph->ncc, &graph->subset_idxs));
    PetscCall(PetscMalloc1(graph->cptr[graph->ncc], &graph->subset_idxs[0]));
    PetscCall(PetscArrayzero(graph->subset_idxs[0], graph->cptr[graph->ncc]));
    for (j = 1; j < graph->ncc; j++) {
      graph->subset_size[j - 1] = graph->cptr[j] - graph->cptr[j - 1];
      graph->subset_idxs[j]     = graph->subset_idxs[j - 1] + graph->subset_size[j - 1];
    }
    graph->subset_size[graph->ncc - 1] = graph->cptr[graph->ncc] - graph->cptr[graph->ncc - 1];
    PetscCall(PetscArraycpy(graph->subset_idxs[0], graph->queue, graph->cptr[graph->ncc]));
  }

  /* renumber reference nodes */
  PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)(graph->l2gmap)), graph->ncc, graph->subset_ref_node, PETSC_COPY_VALUES, &subset_n));
  PetscCall(ISLocalToGlobalMappingApplyIS(graph->l2gmap, subset_n, &subset));
  PetscCall(ISDestroy(&subset_n));
  PetscCall(ISRenumber(subset, NULL, NULL, &subset_n));
  PetscCall(ISDestroy(&subset));
  PetscCall(ISGetLocalSize(subset_n, &k));
  PetscCheck(k == graph->ncc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid size of new subset! %" PetscInt_FMT " != %" PetscInt_FMT, k, graph->ncc);
  PetscCall(ISGetIndices(subset_n, &is_indices));
  PetscCall(PetscArraycpy(graph->subset_ref_node, is_indices, graph->ncc));
  PetscCall(ISRestoreIndices(subset_n, &is_indices));
  PetscCall(ISDestroy(&subset_n));

  /* free workspace */
  graph->setupcalled = PETSC_TRUE;
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphResetCoords(PCBDDCGraph graph) {
  PetscFunctionBegin;
  if (!graph) PetscFunctionReturn(0);
  PetscCall(PetscFree(graph->coords));
  graph->cdim  = 0;
  graph->cnloc = 0;
  graph->cloc  = PETSC_FALSE;
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphResetCSR(PCBDDCGraph graph) {
  PetscFunctionBegin;
  if (!graph) PetscFunctionReturn(0);
  if (graph->freecsr) {
    PetscCall(PetscFree(graph->xadj));
    PetscCall(PetscFree(graph->adjncy));
  } else {
    graph->xadj   = NULL;
    graph->adjncy = NULL;
  }
  graph->freecsr   = PETSC_FALSE;
  graph->nvtxs_csr = 0;
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphReset(PCBDDCGraph graph) {
  PetscFunctionBegin;
  if (!graph) PetscFunctionReturn(0);
  PetscCall(ISLocalToGlobalMappingDestroy(&graph->l2gmap));
  PetscCall(PetscFree(graph->subset_ncc));
  PetscCall(PetscFree(graph->subset_ref_node));
  if (graph->nvtxs) PetscCall(PetscFree(graph->neighbours_set[0]));
  PetscCall(PetscBTDestroy(&graph->touched));
  PetscCall(PetscFree5(graph->count, graph->neighbours_set, graph->subset, graph->which_dof, graph->special_dof));
  PetscCall(PetscFree2(graph->cptr, graph->queue));
  if (graph->mirrors) PetscCall(PetscFree(graph->mirrors_set[0]));
  PetscCall(PetscFree2(graph->mirrors, graph->mirrors_set));
  if (graph->subset_idxs) PetscCall(PetscFree(graph->subset_idxs[0]));
  PetscCall(PetscFree2(graph->subset_size, graph->subset_idxs));
  PetscCall(ISDestroy(&graph->dirdofs));
  PetscCall(ISDestroy(&graph->dirdofsB));
  if (graph->n_local_subs) PetscCall(PetscFree(graph->local_subs));
  graph->has_dirichlet       = PETSC_FALSE;
  graph->twodimset           = PETSC_FALSE;
  graph->twodim              = PETSC_FALSE;
  graph->nvtxs               = 0;
  graph->nvtxs_global        = 0;
  graph->n_subsets           = 0;
  graph->custom_minimal_size = 1;
  graph->n_local_subs        = 0;
  graph->maxcount            = PETSC_MAX_INT;
  graph->setupcalled         = PETSC_FALSE;
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphInit(PCBDDCGraph graph, ISLocalToGlobalMapping l2gmap, PetscInt N, PetscInt maxcount) {
  PetscInt n;

  PetscFunctionBegin;
  PetscValidPointer(graph, 1);
  PetscValidHeaderSpecific(l2gmap, IS_LTOGM_CLASSID, 2);
  PetscValidLogicalCollectiveInt(l2gmap, N, 3);
  PetscValidLogicalCollectiveInt(l2gmap, maxcount, 4);
  /* raise an error if already allocated */
  PetscCheck(!graph->nvtxs_global, PetscObjectComm((PetscObject)l2gmap), PETSC_ERR_PLIB, "BDDCGraph already initialized");
  /* set number of vertices */
  PetscCall(PetscObjectReference((PetscObject)l2gmap));
  graph->l2gmap = l2gmap;
  PetscCall(ISLocalToGlobalMappingGetSize(l2gmap, &n));
  graph->nvtxs        = n;
  graph->nvtxs_global = N;
  /* allocate used space */
  PetscCall(PetscBTCreate(graph->nvtxs, &graph->touched));
  PetscCall(PetscMalloc5(graph->nvtxs, &graph->count, graph->nvtxs, &graph->neighbours_set, graph->nvtxs, &graph->subset, graph->nvtxs, &graph->which_dof, graph->nvtxs, &graph->special_dof));
  /* zeroes memory */
  PetscCall(PetscArrayzero(graph->count, graph->nvtxs));
  PetscCall(PetscArrayzero(graph->subset, graph->nvtxs));
  /* use -1 as a default value for which_dof array */
  for (n = 0; n < graph->nvtxs; n++) graph->which_dof[n] = -1;
  PetscCall(PetscArrayzero(graph->special_dof, graph->nvtxs));
  /* zeroes first pointer to neighbour set */
  if (graph->nvtxs) graph->neighbours_set[0] = NULL;
  /* zeroes workspace for values of ncc */
  graph->subset_ncc      = NULL;
  graph->subset_ref_node = NULL;
  /* maxcount for cc */
  graph->maxcount        = maxcount;
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphDestroy(PCBDDCGraph *graph) {
  PetscFunctionBegin;
  PetscCall(PCBDDCGraphResetCSR(*graph));
  PetscCall(PCBDDCGraphResetCoords(*graph));
  PetscCall(PCBDDCGraphReset(*graph));
  PetscCall(PetscFree(*graph));
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCGraphCreate(PCBDDCGraph *graph) {
  PCBDDCGraph new_graph;

  PetscFunctionBegin;
  PetscCall(PetscNew(&new_graph));
  new_graph->custom_minimal_size = 1;
  new_graph->commsizelimit       = 1;
  *graph                         = new_graph;
  PetscFunctionReturn(0);
}